The hazard rate tangent approximation for boundary hitting times
type: Item
instance of: scholarly article
title: The hazard rate tangent approximation for boundary hitting times
zbMATH Open document ID: 0836.60087
author: Gareth O. Roberts
author: C. F. Shortland
published in: The Annals of Applied Probability
publication date: 1996-04-09T00:00:00Z
review text: The approximation of the distribution of the hitting time \(\tau_f = \inf_{t > 0} \{t : X_t \geq f(t)\}\) of a diffusion process \(X_t\) is considered. When \(X_t\) is the standard Brownian motion \(B_t\), the tangent approximation provides an inaccurate density approximation of \(\tau_f\) by using the Bachelier-Levy formula: \(p^{a,b} (t) = {a \over t^{3/2}} \varphi ({a + bt \over t^{1/2}})\), where \(\varphi\) is the standard Brownian density, \(a = f(t) - tf'(t)\), \(b = f'(t)\). Authors introduce the hazard rate tangent approximation, which considerably improves on the tangent approximation when \(f\) is convex or concave. Numerical examples are also given.
reviewed by: Gong Guanglu
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 60J50
zbMATH DE Number: 811745
zbMATH Keywords: boundary hitting time
zbMATH Keywords: diffusion process
zbMATH Keywords: Brownian motion
zbMATH Keywords: numerical examples
zbMATH Keywords: hazard rate tangent approximation
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aoap/1177004773
OpenAlex ID: W1992130658
DOI: 10.1214/AOAP/1177004773
description: scientific article; zbMATH DE number 811745